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Maurinko [17]
2 years ago
10

The Liu family buys 20 pounds of chicken at the local market for $50. Which equation can be used to represent the cost,

Mathematics
1 answer:
jolli1 [7]2 years ago
5 0

Answer:

Step-by-step explanation:

$50/(20 pounds) = $2.5/pound

C(x) = (x pounds)·$2.5/pound = $2.5x

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Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1
Paladinen [302]

Answer:

D

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

\sqrt{(x+5)^2+(y-5)^2} = | y + 1 |

Squaring both sides

(x + 5)² + (y - 5)² = (y + 1)^2 , that is

(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides

(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify

y² + 2y + 1 - y² + 10y - 25 = (x + 5)²

12y - 24 = (x + 5)² ← factor left side

12(y - 2) = (x + 5)² ← divide both sides by 12

y - 2 = \frac{1}{12} (x + 5)² ← add 2 to both sides

y = \frac{1}{12} (x + 5)² + 2

or

f(x) = \frac{1}{12} (x + 5)² + 2 → D

7 0
3 years ago
3 Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How
Morgarella [4.7K]

Answer:

72

Step-by-step explanation:

The smallest number that is divisible by two given numbers is called the Least Common Multiple (LCM) of those numbers.

What's the smallest number that is a multiple of 8 and also a multiple of 18?

One way to find out is to start making lists of multiples:

Multiples of 8:  8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on,

Multiples of 18:  18, 36, 54, 72, 90, 108, and so on.

This method can be a bit tedious, but in this case, it's clear that 72 is the LCM of 8 and 18.

Another method is to use the <u>prime factorization</u> of the two numbers.

Write 8 and 18 as the product of prime numbers; each number has a unique prime factorization.

8 = 2 x 2 x 2 = 2^3

18 = 2 x 3 x 3 = 2^1 x 3^2

To form the LCM, build a product of primes using the <u>highest exponent</u> in either of the two numbers.

LCM = 2^3 x 3^2 = 8 x 9 = 72.

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